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vaieri [72.5K]
3 years ago
14

Newton’s law of cooling states that the temperature of an object changes at a rate proportionalto the difference between the tem

perature of the object itself and the temperatureof its surroundings (the ambient air temperature in most cases). Suppose that the ambienttemperature is 70◦F and that the rate constant is 0.05 (min)−1.Write a differential equationfor the temperature of the object at any time. Note that the differential equation is thesame whether the temperature of the object is above or below the ambient temperature.
Mathematics
1 answer:
Verizon [17]3 years ago
3 0

Answer:

\frac{dT}{dt} = -0.05\;min^{-1}  (T-70\ºF)

Step-by-step explanation:

Hi!

Lets call:

T = temprature of the object

T₀ = temperature of surroundings

t = time

The rate of change of T is its derivative with respecto to time. If T > T₀, the object looses heat, so T decreases. Then, being k > 0:

\frac{dT}{dt} = -k(T-T_0) \\

In this case T₀ = 70ºF and k = 0.05/min. Then the differential equation is:

\frac{dT}{dt} = -0.05\;min^{-1}  (T-70\ºF)

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Answer:

-4 3/4

Step by step explanation:

point D is 4 numbers to the left of the 0, meaning it is a negative 4. Then there is also a 3/4 of space between the 4 and point D, meaning point D is -4 3/4 away from 0.

6 0
2 years ago
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Jim's backyard is a rectangle that is 15 5/6 yards long and 10 2/5 yards wide. Jim buys sods in pieces that are 1 1/3 yards long
Ne4ueva [31]

We are given

Jim's backyard:

Length is

L=15\frac{5}{6} =\frac{95}{6} yards

width is

W=10\frac{2}{5} =\frac{52}{5} yards

Since, this is rectangle

so, we can find area of rectangle

A=L*W

A=(\frac{95}{6})*(\frac{52}{5})

A=\frac{494}{3} yard^2

Area of one sod:

length is

l=1\frac{1}{3} =\frac{4}{3} yards

width is

w=1\frac{1}{3} =\frac{4}{3} yards

Since, it is rectangle in shape

so,

Area=l*w

A=\frac{4}{3}*\frac{4}{3}

A=\frac{16}{9}yard^2

Number of pieces of sod:

we can use formula

Number of pieces of sod = (area of Jim's backyard)/(area of one sod)

N=\frac{\frac{494}{3} }{\frac{16}{9} }

now, we can simplify it

N=\frac{741}{8} pieces need ..............Answer

7 0
3 years ago
There is a construction zone on a highway. The speeds of vehicles passing through this construction zone are normally distribute
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The percentage of vehicles passing through this construction zone that are traveling at a speed of 50 and 57 miles per hour
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The general form of the equation of a circle is ax2 by2 cx dy e = 0, where a = b 0. if the circle has a radius of 3 units and th
aev [14]

The set of values which might correspond to the circle are A = 1, B = 1, C = 0, D = -8 and E = 7.

<h3>The equation of a circle.</h3>

Mathematically, the general form of the equation of a circle is given by;

(x - h)² + (y - k)² = r²

<u>Where:</u>

  • h and k represents the coordinates at the center.
  • r is the radius of a circle.

Based on the information provided that the center of the circle lies on the y-axis, we have:

(h, k) = (0, 4)

Radius, r = 3 units.

Substituting the given parameters into the formula, we have;

(x - 0)² + (y - 4)² = 3²

x ² + y² - 8y + 16 = 9

x ² + y² - 8y + 7 = 0.

Therefore, the set of values which might correspond to the circle are A = 1, B = 1, C = 0, D = -8 and E = 7.

Read more on circle here: brainly.com/question/1615837

#SPJ1

<u>Complete Question:</u>

The general form of the equation of a circle is Ax² + By² + Cx + Dy + E = 0, where A = B. If the circle has a radius of 3 units and the center at (0, 4), which set of values of A, B, C, D, and E correspond to the circle?

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Which of the following is a polynomial?
Alekssandra [29.7K]

Answer: B

Step-by-step explanation:

When B is simplified, it becomes x^2-3x-10.  This is a polynomial because it has more than two terms(3).

Hope it helps <3

5 0
3 years ago
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